Learn Dutch: Zoek je oude platen van vinyl? Ik heb er gisteren vijf zeldzame bemachtigd. - Are you looking for old vinyl records? I acquired five rare ones yesterday.

This is the quantitative er. Whenever you state a specific quantity of something previously mentioned (here, vijf zeldzame) but drop the noun itself (platen), Dutch requires you to use er. It translates roughly to "of them".

Why does zeldzame end in -e if there is no noun after it?

Even though the noun is left out to avoid repetition, it is still grammatically present in the background (vijf zeldzame platen). Because platen is plural, the adjective keeps its standard -e ending.

Why doesn't the past participle bemachtigd start with ge-?

The infinitive of this verb is bemachtigen (to acquire or get hold of). Because it starts with the inseparable prefix be-, it does not take the standard ge- prefix when forming the past participle.

Could I say vinylplaten instead of platen van vinyl?

Yes, vinylplaten is a completely correct and very common compound noun. Using platen van vinyl means exactly the same thing, but places a little more emphasis on the material itself.